Solving Systems of Equations Without a Graph

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Objective

Students will be able to solve a system of equations algebraically by substituting one equation into the other in order to have an equation in one variable. Students will become fluent in this algebraic technique and will conceptually understand the reasoning behind using the substitution technique.

Big Idea

I really like this lesson because of the scaffolds that are in place in the beginning of the lesson. The examples are very simple but really force students to think about what it means to "substitute" one thing for another. Then, once the problem becomes

Lesson Author

James Bialasik

Amherst, NY

Grade Level

Ninth grade

Subjects

Math

Systems of Equations and Inequalities

Algebra

Standards

HSA-REI.C.5

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

HSA-REI.C.6

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

HSA-REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Opening

10 minutes

Direct Instruction

10 minutes

Independent Practice

15 minutes

Closure

5 minutes

Choose one problem from your independent practice and write out in words why you solved it the way you did. List the steps and a reason for each step" If some students in your class struggle with writing they can explain their description to you. This task will determine which students are understanding the substitution method and which students have only memorized the procedure.

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